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How to find pattern in the following polynomials with mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg104108] How to find pattern in the following polynomials with mathematica
• From: barefoot gigantor <barefoot1980 at gmail.com>
• Date: Mon, 19 Oct 2009 07:13:38 -0400 (EDT)

1:
 1+ (6n + 5)/(12n^2 + 12n + 1)

2:

1+ (150n^2 + 200n + 55)/(300 n^3 + 450 n^2 + 160 n + 5)

3:

1+ (420 n^3+770 n^2+410 n+57) / (840 n^4+1680 n^3+1030 n^2+190 n+3)

4:
1+ (630 n^4+1470 n^3+1155 n^2+343 n+29)/(1260 n^5+3150 n^4+2730 n^3+945
n^2+107 n+1)

5:
1 + (13860 n^5+39270 n^4 + 40740 n^3+18711 n^2+3591 n+205)/(27720 n^6+83160
n^5+93030 n^4+47460 n^3+10689 n^2+819 n+5)